[B1] GENERAL TOPOLOGY 1995/96
Literature
G.Simmons. Introduction to Topology and Modern
Analysis. McGraw-Hill,1963
Schedule
- 25 March
- Introduction. The subject of Topology. Sets, relations and
operations.
- Problems. 1 3 a,b,c; 2 1,3,5.
- 28 March
- Functions. Products of sets.
- Problems. 3 1,2,3,4;
4 1.
-
29 March
- Relations. Equivalence. Theorem of Schröder-Bernstein. Countable sets.
- Problems 5 1,2,4,5; 7 1,3,6,7,8.
-
9 April
- Uncountable sets. Continuum. Real numbers.
- Problems: 7
: 1,2,3,5.
-
11 April
- Metric spaces. Examples. Properties of open sets.
- Problems: 9 1,4,5,6; 10 1,2,5,7,9.
-
12 April
- Closed sets.
- Problems: 11 1,2,4,7,10,13.
-
15 April
- Convergence and completeness in metric spaces.
- Problems 12
1,3,4,7.
- Continuous mappings.
- Problems: 13 1,2,3,6,8,9.
-
18 April
- Spaces of continuous functions. Normed and Banach spaces.
- Problems: 14 1,2,3,5.
-
19 April
- Euclidean and unitary spaces.
- Problems: 15 1,3,4.
-
22 April
- Definition of Topological spaces.
- Problems. 16 1,2,3,5,6,8,9,10,11.
-
25 April
- Closed sets in topological spaces.
- Problems 17 1,2,3,6,7,9.
-
26 April
- Bases of topology.
- Problems. 18 2,3, 4,7,8,9.
- Function algebras.
-
29 April
- Compact spaces: main properties.
- Problems: 21 1,2,4,6,7,8,9.
-
30 April
- Products of spaces. Tikhonov's theorem.
- Problems: 22 1,5; 23 3,4.
-
3 May
- Compactness in metric spaces.
- Problems: 24 3,4. Ascoli's theorem.
-
6 May
- T1 and Hausdorff spaces.
- Problems: 26 1,2,4,5,6,8
-
9 May
- Regular and normal spaces. Extension theorems.
- Problems: 27 1,2,3; 28 3.
-
10 May
- Connected spaces.
- Problems:
31 1,3,4.
- Components.
- Problems: 32 1,4,5,6
-
13 May
- Stone-Weierstrass Theorem.
-
14 May
- Locally compact Hausdorff spaces.
- Problems: 37 1,3
Additional topics are obligatory for PhD students
-
20 May
- The notion of homotopy. Homotopic mappings.
- Problems of topological and Homotopical classification.
-
21 May
- Mappings in Euclidean space. Invertibility.
-
23 May
- Smooth manifolds. Compact manifolds.
-
27 May
- The method of algebraic topology. The fundamental group.
-
28 May
- Coverings. Calculation of fundamental groups. Applications.
Grigori Rozenblioum
<grigori@math.chalmers.se>
Lars Alexandersson <larsa@math.chalmers.se>
Last modified April 26, 1996